How 250 kg of air lifts a car: the Roadster thruster math

By our estimate, 250 kg of compressed air can push the new Tesla Roadster at full thrust for only about two seconds. That is enough for a launch, a hop of a few stories, or a flip with a soft landing, but not for real flight. These are our own calculations, not Tesla's, and every assumption is listed below so you can check them.

How a cold-gas thruster works

Picture a balloon you let go of, made far stronger. Air squeezed very tight in a tank rushes out of a nozzle. The air goes one way and the car is pushed the other way. Nothing burns. SpaceX uses this kind of thruster to steer its rockets (TechCrunch).

The push depends on two things: how many kilograms of air leave each second, and how fast they leave. Multiply the two and you get the force:

Force (newtons) = air used per second (kg/s) × exhaust speed (m/s)

A newton is a unit of force. One kilonewton (kN) is 1,000 newtons, about the weight of a 100 kg object here on Earth.

What Tesla told us, and what we had to assume

Tesla has published very few numbers about the thrusters. Here is what we used.

Input	Value we used	Where it comes from
Air on board	250 kg	Reported by Paultan and CarBuzz from Tesla's Lars Moravy. Two outlets say 260 kg (Investing.com).
Tank volume	600 liters	Reported by TechCrunch, Paultan and CarBuzz
Rear thrust	80 kN	Tesla claim of "over 80 kilonewtons" (Paultan, Jalopnik)
Car mass	2,000 kg (about 4,400 lb)	Our assumption. Tesla has not published a weight. TechCrunch reports Marques Brownlee quoted Tesla as calling it a "4000+ pound car" (TechCrunch). Glitchwire says about two tons (Glitchwire).
Exhaust speed	600 m/s (range 500 to 700)	Our estimate. See below.
Tank pressure	Not stated	Tesla gave none. Musk said 10,000 psi back in 2018 (Wikipedia).

Why 600 m/s? We worked out the top speed room-temperature air can reach when it expands from a tank into a vacuum. Using the standard formula for an ideal nozzle, that ceiling is about 770 m/s. A real nozzle at sea level gets less. The air also chills as the tank empties, which slows it further. For nitrogen, a gas very close to air, Wikipedia's reference table lists a measured cold-gas figure that works out to about 716 m/s in a vacuum (Wikipedia: cold gas thruster). We use 600 m/s as a middle value and show 500 and 700 m/s as low and high cases.

Result 1: full thrust lasts about two seconds

To make 80,000 newtons at 600 m/s, the nozzles must release:

80,000 ÷ 600 = about 133 kg of air per second

With 250 kg on board:

250 ÷ 133 = about 1.9 seconds

At 500 m/s the answer is about 1.6 seconds. At 700 m/s it is about 2.2 seconds. Either way, flat-out thrust ends in around two seconds.

Result 2: a hover would last single-digit seconds

Holding a car still in the air takes less force than a full-power launch. You only need to match its weight.

• Weight of a 2,000 kg car: 2,000 × 9.81 = about 19,600 newtons (19.6 kN)
• Total push stored in the tank: 250 kg × 600 m/s = 150,000 newton-seconds
• Longest possible hover: 150,000 ÷ 19,600 = about 7.6 seconds

The range is 6.4 to 8.9 seconds, depending on exhaust speed. The car gets a little lighter as air leaves, which helps a bit. Several things cut the time down more. Thrust drops as tank pressure falls (Wikipedia: cold gas thruster). Some air goes to steering. And air must be saved for landing. A real hover would be shorter than this ceiling. Tesla has not given any flight time (Investing.com).

Result 3: how high one hop could go

This one needs an extra assumption. The 80 kN figure is for the rear thrusters. Tesla has not said how hard the four downward-facing corner nozzles push. For this example, we assume they could match 80 kN together.

Fire straight down for half a second:

• Upward push minus weight: 80,000 − 19,600 = 60,400 N
• Upward acceleration: 60,400 ÷ 2,000 = about 30 m/s², or about 3 g
• Speed after 0.5 s: about 15 m/s
• Height gained during the burn: about 3.8 m
• Extra height while coasting up: 15² ÷ (2 × 9.81) = about 11.6 m
• Total: about 15 m, or 50 feet, using about 67 kg of air

Coming back down from 15 m, the car would hit about 17 m/s (38 mph). Braking that with the same thrust takes about 0.6 seconds and roughly 77 kg more air. So one 15 m hop with a soft landing uses about 144 kg, more than half the tank.

For comparison, Paultan estimated the kickflip peaked at about 7 meters (Paultan). That fits well inside what the air could do, especially since the car launched off a ramp.

Result 4: the fall off the upside-down ramp

Paultan put the top of the ramp at about 21 m and reported the thrusters braked the fall at up to 3.3 g (Paultan).

If the car fell the full 21 m, it would reach about 20 m/s (45 mph). Our numbers give a braking rate of about 3 g from 80 kN on a 2,000 kg car. At that rate, stopping takes about 0.7 seconds, about 7 m of height, and about 90 kg of air. Our 3 g is close to the 3.3 g Paultan reported, which suggests our inputs are in the right range.

Result 5: the 0-60 claims

Sixty mph is 26.8 m/s.

• Thrust alone: 80,000 ÷ 2,000 = 40 m/s², about 4 g. That reaches 60 mph in about 0.67 seconds.
• Add tire grip of about 1.26 g, a figure from Lars Moravy (Paultan), and the total is about 52 m/s². That reaches 60 mph in about 0.51 seconds.

So Tesla's Rocket claim of under 0.59 seconds is possible on paper, if everything works perfectly. If the thrusters ran flat out for the whole live run of 0.81 seconds, they would use about 108 kg of air, over 40% of the tank.

One number that does not quite add up. Tesla says the thrusters make "4–5x the force the tires can" (Fox Business). Tires gripping at 1.26 g on a 2,000 kg car push with about 24.7 kN. Our 80 kN is about 3.2 times that. Tesla's ratio could reflect more than 80 kN (it said "over 80"), a lighter car, or comparison with ordinary tire grip. Tesla has not shown its math.

Result 6: how hard is the air squeezed?

250 kg of air in 600 liters works out to about 417 kg per cubic meter. Ordinary air weighs about 1.2 kg per cubic meter. So the tank holds air about 350 times denser than the air around you.

At these pressures air does not follow the simple gas law, so we used published real-gas data for air at room temperature. That density needs about 440 bar, roughly 6,400 psi. A car tire holds about 2 bar. This is our estimate. It assumes 600 liters is the inside volume of the tanks. Tesla stated no pressure, and Paultan estimated "several hundred bar" (Paultan).

Result 7: the energy to refill it

Musk said, "The car can recharge its air tank" (Paultan). Tesla has not said how or how fast.

Squeezing 250 kg of air from normal pressure to about 440 bar takes at least about 35 kWh of energy, even in a perfect compressor. Real compressors lose a lot of energy as heat, so a real refill would likely take well more than that. For scale, Kelley Blue Book lists the Model S Plaid battery at 100 kWh (Kelley Blue Book). The Roadster's battery size has not been announced. A full refill from the car's own battery would use a large share of it. That may be why the refill details matter so much, and why we want to see Tesla's answer.

What the math tells us

• It is a jump jet, not a plane. Seconds of thrust, a few stories of height, then wheels down.
• Tesla's stunts fit the physics. The heights and braking forces reported at the show are within what 250 kg of air can do.
• The open questions are refill time and real tank pressure. Tesla's answers will tell us how often an owner could actually fly.

Squeezing air is expensive. Cooling with air can be nearly free. On many summer nights the air outside is cooler than the air inside. Our sister app, Cool Cue, made by the same small company as this site, tells you when outside air is cooler than inside, so you can open the windows at night and close them in the morning.

Sources

• TechCrunch: reveal report
• Paultan: reveal report with measurements
• CarBuzz: features and specs
• Jalopnik: reveal analysis
• Investing.com: reveal report
• Glitchwire: air tank report
• Fox Business: reveal report
• Wikipedia: Tesla Roadster (second generation)
• Wikipedia: cold gas thruster
• Kelley Blue Book: 2026 Model S specs
• Our calculations: ideal-nozzle exhaust speed for air at 20 °C; real-gas air density from published equation-of-state data; ideal isothermal compression energy.